MEASUREMENT LAB PURPOSE:
The purpose of this lab was to experiment with different measuring devices such as the Vernier caliper and micrometer. It allowed students to practice with volume, density, percent error measurments, and also significant figures. It also helped find ways to minimize error and measure as accurately as possible. HYPOTHESIS:
It is hypothesized that all experimental conversion factors calculated in this lab will be close to the accepted values. Also, it is hypothesized that the Vernier caliper will provide a more accurate measurement than with the ruler. The micrometer will yield the most accurate measurement, having less error than both the ruler and Vernier caliper. APPARATUS:
Ruler Vernier caliper Micrometer Scale Card 2 Blocks 2 Cylinders 2 Spheres PROCEDURE: Part A: Get a card. Using a ruler measure the length and width ten times in centimeters. Then measure the length and width of the same card in inches ten times. Calculate the mean value, average deviation, and percent deviation for each set of data. Next, calculate the area of the card and compare it to the accepted value (2.54 cm/in) to find error and percent error. Part B: Choose a block. Using a ruler measure the length, width, and height of the block three times in centimeters. Then, measure the dimensions of the same block three times in inches. Next, find the average length, width, and height of the block for each set of data. Calculate the volume of the block in both cubic inches and cubic centimeters. Divide the average volume in cubic centimeters by the average volume in cubic inches to get the conversion factor or experimental value. Then compare this experimental value to the accepted value (16.39cm^3/in^3) to find error and calculate percent error. Complete the same procedure again using a different block. Part C: Choose a cylinder. Using a Vernier caliper, measure the length and diameter of the cylinder three times in centimeters. Calculate the average radius and length of the cylinder and use these values to find the volume. Place the cylinder on an electronic scale and record the mass in grams. Then calculate the mass density of the cylinder. Compare the experimental mass density to the accepted mass density (1.24g/cm^3) and find error and percent error. Repeat the procedure with a second cylinder. Part D: Choose a sphere. Using a micrometer, measure the length, diameter, and radius in centimeters. Then place the sphere on a scale to determine the mass in grams. Calculate the mass density of the sphere, and compare it to the accepted mass density (2.406g/cm^3 and 2.563g/cm^3). Calculate error and percent error. Then repeat the entire procedure with a second sphere. DATA: Part A:
Trial
Length L
Width W
Length L
Width W
No.
cm
cm
in
in
1
20.25
8.38
8
3.25
2
20.25
8.38
8
3.25
3
20.25
8.38
8
3.25
4
20.25
8.38
8
3.25
5
20.25
8.38
8
3.25
6
20.25
8.38
8
3.25
7
20.25
8.38
8
3.25
8
20.25
8.38
8
3.25
9
20.25
8.38
8
3.25
10
20.25
8.38
8
3.25
Mean Value
20.25
8.38
8
3.25
LENGTH:
Mean value:20.25 cm_ Mean value: 8in_
Average Deviation: _0 cm Average Deviation:0in % Deviation: 0%_ % Deviation: 0% AREA: Area: 169cm^2 Area: 26in^2_ Experimental conversion factor: 20.25/8 cm/in= 2.5 cm/in_
Accepted Value: _2.540 cm/in
Error: .04cm/in_
% Error: 1.6%_ Part B: BLOCK 1:
Average volume: _64.6 cm^3 Average volume: 4.3in^3_ Experimental conversion factor: _15 cm^3/in^3_ Accepted value: 16.39 cm^3/in^3_
Error: 1.39 cm^3/in^3_
% Error: 8.5% Part C:__ CYLINDER 1
Trial
Length L
Diameter D
Radius R
No.
cm
cm
cm
1
9.71
1.64
0.82
2
9.71
1.64
0.82
3
9.71
1.64
0.82
Mean Value
9.71
1.64
0.82
Volume: _20.51cm^3 Mass: 22.289g_ Experimental Mass Density: _1.1g/cm^3_ Accepted Mass Density: 1.24g/cm^3 Error: _.14g/cm^3_ % Error: _11.29% CYLINDER 2
Trial
Length L
Diameter D
Radius R
No.
cm
cm
cm
1
7.63
1.61
.805
2
7.63
1.61
.805
3
7.63
1.61
.805
Mean Value
7.63
1.61
.805
Volume: 15.5cm^3_
Mass: _17.401g Experimental mass density: 1.12g/cm^3 Accepted Mass Density: _1.24g/cm^3 Error: .12 % Error: _9.7% Part D: SPHERE 1__
Trial
Length L
Diameter D
Radius R
No.
cm
cm
cm
1
2.515
2.515
1.258
2
2.515
2.515
1.258
3
2.515
2.515
1.258
Mean Value
2.515
2.515
1.258
Volume: 8.339cm^3_
Mass: 20.062g_
Experimental Mass Density: _2.406g/cm^3 Accepted Mass Density: 2.7g/cm^3 Error: .294g/ cm^3_ % Error: _12.22%_ SPHERE 2
Trial
Length L
Diameter D
Radius R
No.
cm
cm
cm
1
1.419
1.419
.7095
2
1.419
1.419
.7095
3
1.419
1.419
.7095
Mean Value
1.419
1.419
.7095
Volume: 1.496cm^3_
Mass: _3.049g
Experimental Mass Density: 2.038g/cm^3_
Accepted Mass Density: _2.563g/cm^3 Error: _.53 % Error: 20% ANALYSIS: Part A: Mean Value=(20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25)/10 Average Deviation= l average-each value l Percent Deviation= average deviation/ mean value x100 % Error= (2.54-2.5)/2.54 x100=1.6% Part B: Volume for each block= length x width x height Experimental conversion factor=105cm^3/6.4in^3=16cm^3/in^3 Percent Error: (16.39-16)/(16.39)x100=2.4% Experimental conversion factor= (64.6cm^3)/(4.3in^3)=15 cm^3/in^3 Percent Error: (16.39-15)/(16.39)x100=8.5% Part C: Cylinder Volume=pr^2 x h Experimental conversion factor=22.289g/20.51cm^3=1.1g/cm^3 Percent Error= (1.24-1.1)/(1.24)x100=11.29% Experimental conversion factor=17.401g/15.5cm^3=1.12g/cm^3 Percent Error= (1.24-1.12)/(1.12) x 100 Part D: Sphere volume: 4/3pr^3 Experimental conversion factor=20.062g/8.339cm^3=2.406g/cm^3 Percent Error: (7.8-8.339)/(7.8) x 100 Experimental conversion factor=3.049g/1.496cm^3=2.038g/cm^3 Percent Error: (2.563-2.038)/(2.563) x 100 The analysis shows that the results are fairly accurate. The highest percent error occurred with the second sphere and was only 20%. The percent errors for all other data sets were below 15%, with all but two below 10%. The error may be a result of estimation, incorrect measurements or calculations, and failing to zero the scale before recording mass. CONCLUSION:__
After completing the experiment, the results do not support the original hypothesis. The hypothesis predicted that the greatest degree of error would occur when using the least accurate means of measurment, the ruler in this case. However, Parts A and B were completed using a ruler and they had smaller percent errors. Also, the hypothesis predicted the Vernier caliper would be less accurate than the micrometer but the experiment did not support this either. In Part C measurements were taken using a Vernier caliper and the percent error averaged 10.5%. In Part D a micrometer was used and the percent error averaged 16.11%. In future investigations it would probably be helpful to make sure the note cards were cut evenly and find something to hold the spheres and cylinders in place to ensure more accurate measurements.
PURPOSE:
The purpose of this lab was to experiment with different measuring devices such as the Vernier caliper and micrometer. It allowed students to practice with volume, density, percent error measurments, and also significant figures. It also helped find ways to minimize error and measure as accurately as possible.
HYPOTHESIS:
It is hypothesized that all experimental conversion factors calculated in this lab will be close to the accepted values. Also, it is hypothesized that the Vernier caliper will provide a more accurate measurement than with the ruler. The micrometer will yield the most accurate measurement, having less error than both the ruler and Vernier caliper.
APPARATUS:
Ruler Vernier caliper Micrometer Scale Card 2 Blocks 2 Cylinders 2 Spheres
PROCEDURE:
Part A: Get a card. Using a ruler measure the length and width ten times in centimeters. Then measure the length and width of the same card in inches ten times. Calculate the mean value, average deviation, and percent deviation for each set of data. Next, calculate the area of the card and compare it to the accepted value (2.54 cm/in) to find error and percent error.
Part B: Choose a block. Using a ruler measure the length, width, and height of the block three times in centimeters. Then, measure the dimensions of the same block three times in inches. Next, find the average length, width, and height of the block for each set of data. Calculate the volume of the block in both cubic inches and cubic centimeters. Divide the average volume in cubic centimeters by the average volume in cubic inches to get the conversion factor or experimental value. Then compare this experimental value to the accepted value (16.39cm^3/in^3) to find error and calculate percent error. Complete the same procedure again using a different block.
Part C: Choose a cylinder. Using a Vernier caliper, measure the length and diameter of the cylinder three times in centimeters. Calculate the average radius and length of the cylinder and use these values to find the volume. Place the cylinder on an electronic scale and record the mass in grams. Then calculate the mass density of the cylinder. Compare the experimental mass density to the accepted mass density (1.24g/cm^3) and find error and percent error. Repeat the procedure with a second cylinder.
Part D: Choose a sphere. Using a micrometer, measure the length, diameter, and radius in centimeters. Then place the sphere on a scale to determine the mass in grams. Calculate the mass density of the sphere, and compare it to the accepted mass density (2.406g/cm^3 and 2.563g/cm^3). Calculate error and percent error. Then repeat the entire procedure with a second sphere.
DATA:
Part A:
LENGTH:
Mean value:20.25 cm_ Mean value: 8in_
Average Deviation: _0 cm Average Deviation:0in
% Deviation: 0%_ % Deviation: 0%
AREA:
Area: 169cm^2 Area: 26in^2_
Experimental conversion factor: 20.25/8 cm/in= 2.5 cm/in_
Accepted Value: _2.540 cm/in
Error: .04cm/in_
% Error: 1.6%_
Part B:
BLOCK 1:
Average volume: _10.5cm^3_
Average volume: _6.4in^3
Experimental conversion factor: 16 cm^3/in^3
Accepted value: _16.39 cm^3/in^3_
Error: _0.39 cm^3/in^3_
% Error: 2.4%__
BLOCK 2:
Average volume: _64.6 cm^3
Average volume: 4.3in^3_
Experimental conversion factor: _15 cm^3/in^3_
Accepted value: 16.39 cm^3/in^3_
Error: 1.39 cm^3/in^3_
% Error: 8.5%
Part C:__
CYLINDER 1
Volume: _20.51cm^3
Mass: 22.289g_
Experimental Mass Density: _1.1g/cm^3_
Accepted Mass Density: 1.24g/cm^3
Error: _.14g/cm^3_
% Error: _11.29%
CYLINDER 2
Volume: 15.5cm^3_
Mass: _17.401g
Experimental mass density: 1.12g/cm^3
Accepted Mass Density: _1.24g/cm^3
Error: .12
% Error: _9.7%
Part D:
SPHERE 1__
Volume: 8.339cm^3_
Mass: 20.062g_
Experimental Mass Density: _2.406g/cm^3
Accepted Mass Density: 2.7g/cm^3
Error: .294g/ cm^3_
% Error: _12.22%_
SPHERE 2
Volume: 1.496cm^3_
Mass: _3.049g
Experimental Mass Density: 2.038g/cm^3_
Accepted Mass Density: _2.563g/cm^3
Error: _.53
% Error: 20%
ANALYSIS:
Part A:
Mean Value=(20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25+20.25)/10
Average Deviation= l average-each value l
Percent Deviation= average deviation/ mean value x100
% Error= (2.54-2.5)/2.54 x100=1.6%
Part B:
Volume for each block= length x width x height
Experimental conversion factor=105cm^3/6.4in^3=16cm^3/in^3
Percent Error: (16.39-16)/(16.39)x100=2.4%
Experimental conversion factor= (64.6cm^3)/(4.3in^3)=15 cm^3/in^3
Percent Error: (16.39-15)/(16.39)x100=8.5%
Part C:
Cylinder Volume=pr^2 x h
Experimental conversion factor=22.289g/20.51cm^3=1.1g/cm^3
Percent Error= (1.24-1.1)/(1.24)x100=11.29%
Experimental conversion factor=17.401g/15.5cm^3=1.12g/cm^3
Percent Error= (1.24-1.12)/(1.12) x 100
Part D:
Sphere volume: 4/3pr^3
Experimental conversion factor=20.062g/8.339cm^3=2.406g/cm^3
Percent Error: (7.8-8.339)/(7.8) x 100
Experimental conversion factor=3.049g/1.496cm^3=2.038g/cm^3
Percent Error: (2.563-2.038)/(2.563) x 100
The analysis shows that the results are fairly accurate. The highest percent error occurred with the second sphere and was only 20%. The percent errors for all other data sets were below 15%, with all but two below 10%. The error may be a result of estimation, incorrect measurements or calculations, and failing to zero the scale before recording mass.
CONCLUSION:__
After completing the experiment, the results do not support the original hypothesis. The hypothesis predicted that the greatest degree of error would occur when using the least accurate means of measurment, the ruler in this case. However, Parts A and B were completed using a ruler and they had smaller percent errors. Also, the hypothesis predicted the Vernier caliper would be less accurate than the micrometer but the experiment did not support this either. In Part C measurements were taken using a Vernier caliper and the percent error averaged 10.5%. In Part D a micrometer was used and the percent error averaged 16.11%. In future investigations it would probably be helpful to make sure the note cards were cut evenly and find something to hold the spheres and cylinders in place to ensure more accurate measurements.
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